Common problem or not?

Sounds like a multi-meter and some contact cleaning are in your future.
The radio issue is that the power inside the cabin is less than 12v when idling. I had the same issue with my duster even after going to a 90A alternator. The voltage regulator was/is doing it's job but it might be getting a much "cleaner" voltage from the harness.
The problem points are: bulk head connector, ign switch and connector, and possibly the fuse box.
Another issue that can be nasty is if the regulator is "seeing" low voltage due to bad connections and opens up the alt output too high and smoke stuff.

Each dirty connector will introduce resistance in the line. If you have 12v at the battery at idle you MIGHT get 10-11v inside the car. The charging system should be 12.6v at idle and top out at no more than 15v
Measure what you are getting at the fuse box and then work back toward the battery.
* you can test the voltage drop over the length of a wire by connecting the - lead from the volt meter to the end of the wire and the + lead close to the battery. The voltage displayed will be the voltage drop on that line ( like .5 to 1v )